What is the derivative of 100(1+Ae^{-t})^{-1} ?

The derivative of 100(1+Ae^{-t})^{-1} is (100Ae^{-t})/((1+Ae^{-t))^2}

What is the first derivative of 100(1+Ae^{-t})^{-1} ?

The first derivative of 100(1+Ae^{-t})^{-1} is (100Ae^{-t})/((1+Ae^{-t))^2}

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derivative of

100 (1 + A e^{- t})^{- 1}

\frac{100 A e ^{- t}}{( 1 + A e ^{- t} ) ^{2}}

Solution steps

\frac{d}{d t} (100 (1 + A e^{- t})^{- 1})

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= 100 \frac{d}{d t} ((1 + A e^{- t})^{- 1})

Apply the chain rule:

- \frac{1}{( 1 + A e ^{- t} ) ^{2}} \frac{d}{d t} (1 + A e^{- t})

= - \frac{1}{( 1 + A e ^{- t} ) ^{2}} \frac{d}{d t} (1 + A e^{- t})

\frac{d}{d t} (1 + A e^{- t}) = - A e^{- t}

= 100 (- \frac{1}{( 1 + A e ^{- t} ) ^{2}} (- A e^{- t}))

Simplify

100 (- \frac{1}{( 1 + A e ^{- t} ) ^{2}} (- A e^{- t})) : \frac{100 A e ^{- t}}{( 1 + A e ^{- t} ) ^{2}}

= \frac{100 A e ^{- t}}{( 1 + A e ^{- t} ) ^{2}}

What is the derivative of 100(1+Ae^{-t})^{-1} ?
The derivative of 100(1+Ae^{-t})^{-1} is (100Ae^{-t})/((1+Ae^{-t))^2}
What is the first derivative of 100(1+Ae^{-t})^{-1} ?
The first derivative of 100(1+Ae^{-t})^{-1} is (100Ae^{-t})/((1+Ae^{-t))^2}